The reassigned spectrogram is a special graphic time / frequency representation;
especially suited for "fast" spectrograms. Compared with the classic spectrogram
(aka 'waterfall') display, reassigned spectrograms can offer better resolution
in the time- as well as in the frequency domain.

For example, the following two spectrograms show the same signal, using the
same display parameters (same FFT window, same FFT size, same scroll
interval...):

The reassigned spectrogram shows a much 'sharper' image than the classic
spectrogram, as long as the criteria for
separability are fulfilled, and the signals have
a sufficient signal-to-noise ratio. The principle
of time/frequency reassignment is described further below; several
in-depth articles about the topic can be found
through a websearch.

The display settings, and the configuration of the test signal generator
are contained in the configuration 'reassigned_spectrogram_test.usr' . How
to load such files into SpecLab is explained
here.

A 5-Hz sawtooth function
(the sharp falling edge is visible as narrow vertial line in the reassigned
spectrogram)

An unmodulated frequency sine wave
(move this a bit higher in frequency so it overlaps with the FM'ed sine,
to see what happens without sufficient
separation)

White Gaussian noise, which results in some "background illumination" in
the classic spectrogram, but creates some "wavery structure" in the reassigned
spectrogram (which may be eliminated with a smarter algorithm one fine day...)

Quick Settings .. Reassigned Spectrograms ... frequency- but not time-reassigned
spectrogram
(was only intended for testing purposes, but it's interesting to see the
effect of frequency-reassignment alone)

The classic spectrogram plots the magnitudes found in each frequency bin.
It discards the phase information from the short-time fourier transform.

The reassigned spectrogram tries to "sharpen" the time/frequency display
by using phase information from the complex short-time fourier transform
(STFT).
For example, by comparing the phase between two neighbouring frequency bins
(within the same STFT) it is possible to relocate the energy from that cell
along the time(!) axis.
By comparing the phase in a frequency bin (between two neighbouring STFTs),
it is possible to relocate the energy from that cell along the frequency(!)
axis.

Details, and implementation notes can be found in the literature; some articles
are listed further below.

To use the reassigned spectrogram effectively, one doesn't have to understand
exactly how it works; but it's important to know the
limitations.

In this example, two signals can only be separated (i.e. produce a "good"
time/frequency reassigned spectrogram) if they are separated by at least
129 Hz (in frequency), or by at least 12 milliseconds (in time).

A higher frequency resolution decreases the time resolution, and vice versa.
In this regard, the same limitations exist for the classic spectrogram and
for the reassigned spectrogram. Carefully selecting the optimum FFT size
is essential :

Too large FFT size -> poor time separability, but good frequency separability

Too small FFT size -> poor frequency separability, but good time separability
.

If there is only "one" signal (or a large separation between two signals,
in time and/or frequency), the selection of the FFT size is not as critical
as when there are two or more signals close to each other.

It is advisable to use the
"automatic scroll speed"
for the spectrogram, and use an overlap (between two STFTs) of 50, 75, or
87.5 percent.
Then, the FFT size will also set the scroll speed (aka 'frame advance'),
so there's not too much "smearing" along the time axis.

The preconfigured settings in Spectrum Lab's
Quick Settings menu may
help to find a good starting point for a certain application.